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What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?

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Question: What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?

Options:

  1. (-3, 6, -3)
  2. (-3, 6, 3)
  3. (3, -6, 3)
  4. (3, 6, -3)

Correct Answer: (-3, 6, -3)

Solution: 

Cross product = |i  j  k| |1  2  3| |4  5  6| = (-3, 6, -3).

What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?

Practice Questions

Q1
What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?
  1. (-3, 6, -3)
  2. (-3, 6, 3)
  3. (3, -6, 3)
  4. (3, 6, -3)

Questions & Step-by-Step Solutions

What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?
Correct Answer: (-3, 6, -3)
  • Step 1: Write down the vectors. We have vector A = (1, 2, 3) and vector B = (4, 5, 6).
  • Step 2: Set up the determinant for the cross product using the unit vectors i, j, k. It looks like this: |i j k| |1 2 3| |4 5 6|.
  • Step 3: Calculate the determinant. This involves finding the components of the resulting vector.
  • Step 4: For the i component, calculate: (2*6 - 3*5) = (12 - 15) = -3.
  • Step 5: For the j component, calculate: (3*4 - 1*6) = (12 - 6) = 6. Remember to put a negative sign in front of this component, so it becomes -6.
  • Step 6: For the k component, calculate: (1*5 - 2*4) = (5 - 8) = -3.
  • Step 7: Combine the components to get the final result: (-3, -6, -3).
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